17c478bdstevel@tonic-gate/*
27c478bdstevel@tonic-gate * CDDL HEADER START
37c478bdstevel@tonic-gate *
47c478bdstevel@tonic-gate * The contents of this file are subject to the terms of the
57c478bdstevel@tonic-gate * Common Development and Distribution License, Version 1.0 only
67c478bdstevel@tonic-gate * (the "License").  You may not use this file except in compliance
77c478bdstevel@tonic-gate * with the License.
87c478bdstevel@tonic-gate *
97c478bdstevel@tonic-gate * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
107c478bdstevel@tonic-gate * or http://www.opensolaris.org/os/licensing.
117c478bdstevel@tonic-gate * See the License for the specific language governing permissions
127c478bdstevel@tonic-gate * and limitations under the License.
137c478bdstevel@tonic-gate *
147c478bdstevel@tonic-gate * When distributing Covered Code, include this CDDL HEADER in each
157c478bdstevel@tonic-gate * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
167c478bdstevel@tonic-gate * If applicable, add the following below this CDDL HEADER, with the
177c478bdstevel@tonic-gate * fields enclosed by brackets "[]" replaced with your own identifying
187c478bdstevel@tonic-gate * information: Portions Copyright [yyyy] [name of copyright owner]
197c478bdstevel@tonic-gate *
207c478bdstevel@tonic-gate * CDDL HEADER END
217c478bdstevel@tonic-gate */
227c478bdstevel@tonic-gate/*
237c478bdstevel@tonic-gate * Copyright 2003 Sun Microsystems, Inc.  All rights reserved.
247c478bdstevel@tonic-gate * Use is subject to license terms.
257c478bdstevel@tonic-gate */
267c478bdstevel@tonic-gate
277c478bdstevel@tonic-gate#pragma ident	"%Z%%M%	%I%	%E% SMI"
287c478bdstevel@tonic-gate
297c478bdstevel@tonic-gate/*
307c478bdstevel@tonic-gate * _D_cplx_div_rx(a, w) returns a / w with infinities handled according
317c478bdstevel@tonic-gate * to C99.
327c478bdstevel@tonic-gate *
337c478bdstevel@tonic-gate * If a and w are both finite and w is nonzero, _D_cplx_div_rx(a, w)
347c478bdstevel@tonic-gate * delivers the complex quotient q according to the usual formula:
357c478bdstevel@tonic-gate * let c = Re(w), and d = Im(w); then q = x + I * y where x = (a * c)
367c478bdstevel@tonic-gate * / r and y = (-a * d) / r with r = c * c + d * d.  This implementa-
377c478bdstevel@tonic-gate * tion scales to avoid premature underflow or overflow.
387c478bdstevel@tonic-gate *
397c478bdstevel@tonic-gate * If a is neither NaN nor zero and w is zero, or if a is infinite
407c478bdstevel@tonic-gate * and w is finite and nonzero, _D_cplx_div_rx delivers an infinite
417c478bdstevel@tonic-gate * result.  If a is finite and w is infinite, _D_cplx_div_rx delivers
427c478bdstevel@tonic-gate * a zero result.
437c478bdstevel@tonic-gate *
447c478bdstevel@tonic-gate * If a and w are both zero or both infinite, or if either a or w is
457c478bdstevel@tonic-gate * NaN, _D_cplx_div_rx delivers NaN + I * NaN.  C99 doesn't specify
467c478bdstevel@tonic-gate * these cases.
477c478bdstevel@tonic-gate *
487c478bdstevel@tonic-gate * This implementation can raise spurious underflow, overflow, in-
497c478bdstevel@tonic-gate * valid operation, inexact, and division-by-zero exceptions.  C99
507c478bdstevel@tonic-gate * allows this.
517c478bdstevel@tonic-gate *
527c478bdstevel@tonic-gate * Warning: Do not attempt to "optimize" this code by removing multi-
537c478bdstevel@tonic-gate * plications by zero.
547c478bdstevel@tonic-gate */
557c478bdstevel@tonic-gate
567c478bdstevel@tonic-gate#if !defined(sparc) && !defined(__sparc)
577c478bdstevel@tonic-gate#error This code is for SPARC only
587c478bdstevel@tonic-gate#endif
597c478bdstevel@tonic-gate
607c478bdstevel@tonic-gate/*
617c478bdstevel@tonic-gate * scl[i].d = 2^(250*(4-i)) for i = 0, ..., 9
627c478bdstevel@tonic-gate */
637c478bdstevel@tonic-gatestatic const union {
647c478bdstevel@tonic-gate	int	i[2];
657c478bdstevel@tonic-gate	double	d;
667c478bdstevel@tonic-gate} scl[9] = {
677c478bdstevel@tonic-gate	{ 0x7e700000, 0 },
687c478bdstevel@tonic-gate	{ 0x6ed00000, 0 },
697c478bdstevel@tonic-gate	{ 0x5f300000, 0 },
707c478bdstevel@tonic-gate	{ 0x4f900000, 0 },
717c478bdstevel@tonic-gate	{ 0x3ff00000, 0 },
727c478bdstevel@tonic-gate	{ 0x30500000, 0 },
737c478bdstevel@tonic-gate	{ 0x20b00000, 0 },
747c478bdstevel@tonic-gate	{ 0x11100000, 0 },
757c478bdstevel@tonic-gate	{ 0x01700000, 0 }
767c478bdstevel@tonic-gate};
777c478bdstevel@tonic-gate
787c478bdstevel@tonic-gate/*
797c478bdstevel@tonic-gate * Return +1 if x is +Inf, -1 if x is -Inf, and 0 otherwise
807c478bdstevel@tonic-gate */
817c478bdstevel@tonic-gatestatic int
827c478bdstevel@tonic-gatetestinf(double x)
837c478bdstevel@tonic-gate{
847c478bdstevel@tonic-gate	union {
857c478bdstevel@tonic-gate		int	i[2];
867c478bdstevel@tonic-gate		double	d;
877c478bdstevel@tonic-gate	} xx;
887c478bdstevel@tonic-gate
897c478bdstevel@tonic-gate	xx.d = x;
907c478bdstevel@tonic-gate	return (((((xx.i[0] << 1) - 0xffe00000) | xx.i[1]) == 0)?
917c478bdstevel@tonic-gate		(1 | (xx.i[0] >> 31)) : 0);
927c478bdstevel@tonic-gate}
937c478bdstevel@tonic-gate
947c478bdstevel@tonic-gatedouble _Complex
957c478bdstevel@tonic-gate_D_cplx_div_rx(double a, double _Complex w)
967c478bdstevel@tonic-gate{
977c478bdstevel@tonic-gate	double _Complex	v;
987c478bdstevel@tonic-gate	union {
997c478bdstevel@tonic-gate		int	i[2];
1007c478bdstevel@tonic-gate		double	d;
1017c478bdstevel@tonic-gate	} aa, cc, dd;
1027c478bdstevel@tonic-gate	double		c, d, sc, sd, r;
1037c478bdstevel@tonic-gate	int		ha, hc, hd, hw, i, j;
1047c478bdstevel@tonic-gate
1057c478bdstevel@tonic-gate	/*
1067c478bdstevel@tonic-gate	 * The following is equivalent to
1077c478bdstevel@tonic-gate	 *
1087c478bdstevel@tonic-gate	 *  c = creal(w); d = cimag(w);
1097c478bdstevel@tonic-gate	 */
1107c478bdstevel@tonic-gate	c = ((double *)&w)[0];
1117c478bdstevel@tonic-gate	d = ((double *)&w)[1];
1127c478bdstevel@tonic-gate
1137c478bdstevel@tonic-gate	/* extract high-order words to estimate |a| and |w| */
1147c478bdstevel@tonic-gate	aa.d = a;
1157c478bdstevel@tonic-gate	ha = aa.i[0] & ~0x80000000;
1167c478bdstevel@tonic-gate
1177c478bdstevel@tonic-gate	cc.d = c;
1187c478bdstevel@tonic-gate	dd.d = d;
1197c478bdstevel@tonic-gate	hc = cc.i[0] & ~0x80000000;
1207c478bdstevel@tonic-gate	hd = dd.i[0] & ~0x80000000;
1217c478bdstevel@tonic-gate	hw = (hc > hd)? hc : hd;
1227c478bdstevel@tonic-gate
1237c478bdstevel@tonic-gate	/* check for special cases */
1247c478bdstevel@tonic-gate	if (hw >= 0x7ff00000) { /* w is inf or nan */
1257c478bdstevel@tonic-gate		i = testinf(c);
1267c478bdstevel@tonic-gate		j = testinf(d);
1277c478bdstevel@tonic-gate		if (i | j) { /* w is infinite */
1287c478bdstevel@tonic-gate			c = (cc.i[0] < 0)? -0.0 : 0.0;
1297c478bdstevel@tonic-gate			d = (dd.i[0] < 0)? -0.0 : 0.0;
1307c478bdstevel@tonic-gate		} else /* w is nan */
1317c478bdstevel@tonic-gate			a *= c * d;
1327c478bdstevel@tonic-gate		((double *)&v)[0] = a * c;
1337c478bdstevel@tonic-gate		((double *)&v)[1] = -a * d;
1347c478bdstevel@tonic-gate		return (v);
1357c478bdstevel@tonic-gate	}
1367c478bdstevel@tonic-gate
1377c478bdstevel@tonic-gate	if (hw < 0x00100000) {
1387c478bdstevel@tonic-gate		/*
1397c478bdstevel@tonic-gate		 * This nonsense is needed to work around some SPARC
1407c478bdstevel@tonic-gate		 * implementations of nonstandard mode; if both parts
1417c478bdstevel@tonic-gate		 * of w are subnormal, multiply them by one to force
1427c478bdstevel@tonic-gate		 * them to be flushed to zero when nonstandard mode
1437c478bdstevel@tonic-gate		 * is enabled.  Sheesh.
1447c478bdstevel@tonic-gate		 */
1457c478bdstevel@tonic-gate		cc.d = c = c * 1.0;
1467c478bdstevel@tonic-gate		dd.d = d = d * 1.0;
1477c478bdstevel@tonic-gate		hc = cc.i[0] & ~0x80000000;
1487c478bdstevel@tonic-gate		hd = dd.i[0] & ~0x80000000;
1497c478bdstevel@tonic-gate		hw = (hc > hd)? hc : hd;
1507c478bdstevel@tonic-gate	}
1517c478bdstevel@tonic-gate
1527c478bdstevel@tonic-gate	if (hw == 0 && (cc.i[1] | dd.i[1]) == 0) {
1537c478bdstevel@tonic-gate		/* w is zero; multiply a by 1/Re(w) - I * Im(w) */
1547c478bdstevel@tonic-gate		c = 1.0 / c;
1557c478bdstevel@tonic-gate		i = testinf(a);
1567c478bdstevel@tonic-gate		if (i) { /* a is infinite */
1577c478bdstevel@tonic-gate			a = i;
1587c478bdstevel@tonic-gate		}
1597c478bdstevel@tonic-gate		((double *)&v)[0] = a * c;
1607c478bdstevel@tonic-gate		((double *)&v)[1] = (a == 0.0)? a * c : -a * d;
1617c478bdstevel@tonic-gate		return (v);
1627c478bdstevel@tonic-gate	}
1637c478bdstevel@tonic-gate
1647c478bdstevel@tonic-gate	if (ha >= 0x7ff00000) { /* a is inf or nan */
1657c478bdstevel@tonic-gate		((double *)&v)[0] = a * c;
1667c478bdstevel@tonic-gate		((double *)&v)[1] = -a * d;
1677c478bdstevel@tonic-gate		return (v);
1687c478bdstevel@tonic-gate	}
1697c478bdstevel@tonic-gate
1707c478bdstevel@tonic-gate	/*
1717c478bdstevel@tonic-gate	 * Compute the real and imaginary parts of the quotient,
1727c478bdstevel@tonic-gate	 * scaling to avoid overflow or underflow.
1737c478bdstevel@tonic-gate	 */
1747c478bdstevel@tonic-gate	hw = (hw - 0x38000000) >> 28;
1757c478bdstevel@tonic-gate	sc = c * scl[hw + 4].d;
1767c478bdstevel@tonic-gate	sd = d * scl[hw + 4].d;
1777c478bdstevel@tonic-gate	r = sc * sc + sd * sd;
1787c478bdstevel@tonic-gate
1797c478bdstevel@tonic-gate	ha = (ha - 0x38000000) >> 28;
1807c478bdstevel@tonic-gate	a = (a * scl[ha + 4].d) / r;
1817c478bdstevel@tonic-gate	ha -= (hw + hw);
1827c478bdstevel@tonic-gate
1837c478bdstevel@tonic-gate	hc = (hc - 0x38000000) >> 28;
1847c478bdstevel@tonic-gate	c = (c * scl[hc + 4].d) * a;
1857c478bdstevel@tonic-gate	hc += ha;
1867c478bdstevel@tonic-gate
1877c478bdstevel@tonic-gate	hd = (hd - 0x38000000) >> 28;
1887c478bdstevel@tonic-gate	d = -(d * scl[hd + 4].d) * a;
1897c478bdstevel@tonic-gate	hd += ha;
1907c478bdstevel@tonic-gate
1917c478bdstevel@tonic-gate	/* compensate for scaling */
1927c478bdstevel@tonic-gate	sc = scl[3].d; /* 2^250 */
1937c478bdstevel@tonic-gate	if (hc < 0) {
1947c478bdstevel@tonic-gate		hc = -hc;
1957c478bdstevel@tonic-gate		sc = scl[5].d; /* 2^-250 */
1967c478bdstevel@tonic-gate	}
1977c478bdstevel@tonic-gate	while (hc--)
1987c478bdstevel@tonic-gate		c *= sc;
1997c478bdstevel@tonic-gate
2007c478bdstevel@tonic-gate	sd = scl[3].d;
2017c478bdstevel@tonic-gate	if (hd < 0) {
2027c478bdstevel@tonic-gate		hd = -hd;
2037c478bdstevel@tonic-gate		sd = scl[5].d;
2047c478bdstevel@tonic-gate	}
2057c478bdstevel@tonic-gate	while (hd--)
2067c478bdstevel@tonic-gate		d *= sd;
2077c478bdstevel@tonic-gate
2087c478bdstevel@tonic-gate	((double *)&v)[0] = c;
2097c478bdstevel@tonic-gate	((double *)&v)[1] = d;
2107c478bdstevel@tonic-gate	return (v);
2117c478bdstevel@tonic-gate}
212